Illustrating Rational Algebraic Expressions
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This document focuses on grade 8 mathematics, specifically addressing the illustration, evaluation, and conditions under which rational algebraic expressions become undefined. It provides definitions and examples of evaluating expressions and explains how to determine values that make expressions undefined by equating the denominator to zero. Additionally, it includes practice problems for students to test their understanding of these concepts.
Illustrating Rational Algebraic Expressions
- 1. Grade 8 – Mathematics Quarter I ILLUSTRATING RATIONAL ALGEBRAIC EXPRESSIONS
- 2. 1. illustrate rational algebraic expressions; 2. evaluate rational algebraic expressions, and 3. find every value of the variables that makes a rational expression undefined.
- 3. RATIONAL ALGEBRAIC EXPRESSIONS - A rational expression in one variable is an expression that can be written in the form 𝑷 𝑸 , where P and Q are polynomials. 𝟒 𝒙 −𝟐 𝒙 𝟐 + 𝟐𝒙 − 𝟑𝟓 𝟑𝒙 + 𝟒 𝟒𝒙 𝒙 𝟐 + 𝟗 not UNDEFINEDRemember, Q ≠ 0,
- 4. EVALUATING ALGEBRAIC EXPRESSIONS Evaluate the expression 𝒙 𝟐− 𝟒 𝒙 −𝟐 when… = 𝒙 𝟐− 𝟒 𝒙 −𝟐 x = 0 = ( ) 𝟐− 𝟒 ( ) −𝟐 0 0 = − 𝟒 −𝟐 = 2 = 𝒙 𝟐− 𝟒 𝒙 −𝟐 x = 1 = ( ) 𝟐− 𝟒 ( ) −𝟐 = − 𝟑 −𝟏 = 3 1 1 = 𝟏− 𝟒 𝟏−𝟐
- 5. EVALUATING ALGEBRAIC EXPRESSIONS Evaluate the expression 𝒙 𝟐−𝟐 𝒙 −𝟒 when… = 𝒙 𝟐−𝟐 𝒙 −𝟒 x = 1 = ( ) 𝟐−𝟐 − 𝟒 1 1 = 𝟏−𝟐 𝟏−𝟒 = 𝟏 𝟑 = 𝒙 𝟐− 𝟒 𝒙 −𝟐 x = 2 = ( ) 𝟐−𝟐 −𝟒 = 𝟐 −𝟐 = -1 2 2 = 𝟒 −𝟐 𝟐 − 𝟒 = −𝟏 −𝟑
- 6. EVALUATING ALGEBRAIC EXPRESSIONS Evaluate the expression 𝒂 𝟐−𝟐𝒃 𝒂 −𝒃 when… = 𝒂 𝟐−𝟐𝒃 𝒂 −𝒃 a = 1 b = 2 = ( ) 𝟐−𝟐( ) −( ) 1 1 = 𝟏−𝟒 𝟏−𝟐 = 3= −𝟑 −𝟏 2 2 = 𝒂 𝟐−𝟐𝒃 𝒂 −𝒃 a = 2 b = 3 = ( ) 𝟐−𝟐( ) −( ) 2 2 = 𝟒−𝟔 𝟐−𝟑 = 2= −𝟐 −𝟏 3 3
- 7. UNDEFINED To make a rational expression 𝒙 𝟐−𝟐 𝒙 −𝟒 UNDEFINED, x – 4 = 0equate the denominator to zero solve for the variable x = 0 + 4 x = 4 The expression 𝒙 𝟐−𝟐 𝒙 −𝟒 is UNDEFINED if x is replaced by 4, because the denominator would be 0.
- 8. UNDEFINED To make a rational expression 𝒙 𝟐−𝟒 𝒙 −𝟐 UNDEFINED, x – 2 = 0equate the denominator to zero solve for the variable x = 0 + 2 x = 2 The expression 𝒙 𝟐−𝟒 𝒙 −𝟐 is UNDEFINED if x is replaced by 2, because the denominator would be 0.
- 9. UNDEFINED To make a rational expression 𝒙 𝟐−𝒚 𝒙 −𝒚 UNDEFINED, x – y = 0equate the denominator to zero solve for the variable x = 0 + y x = y The expression 𝒙 𝟐−𝒚 𝒙 −𝒚 is UNDEFINED if the variables x and y are replaced by equal values.
- 10. Test Yourself. 1. Explain how to evaluate an algebraic expression. 2. What causes a rational expression to be undefined? 3. How do you find the values that may cause a rational expression to be undefined?
- 11. Test Yourself. I. Evaluate each rational expression if a = 1 and b = 2 1. 𝑎 𝑏2 2. 2𝑎−𝑏 3𝑎𝑏 II. Find the value of the variable that makes the expression undefined. 1. 3𝑎 4𝑏 2. 2𝑎−𝑏 𝑏−3